In this work we assume classifiers \(f\)  output a probability vector \(f(x)\)  over the candidate classes \(\)  and treat
confidence as a scalar quantity \(c(f(x)) \in [0,1]\)  that represents how confident \(f\)  is in its prediction, with scores near 1 representing highly confident predictions. Intuitively, a good confidence measure should give rise to scores that correlate well with the accuracy of \(f\) . In Section  we show that this objective can be decomposed into two familiar terms from the literature on forecasting [1]}, [2]}: a calibration error term (encouraging that whenever we output a confidence value of e.g. 0.7, then on average, 70% of the time the model makes a correct prediction) and a sharpness term (encouraging the confidence values to also be varied).
